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Cogito

Integrated Math 2 · Chapter 8 · Lesson 2

Practice Worksheet

Conditional Probability

Given that something already happened.

12 problems · about 21 minutes · S-CP.A.3, S-CP.B.6

NameDate

Figure — use these to answer the problems

Conditioning means using one bar as the new total rather than the sum of them all.
Group A12
Group B8
Group A12
Group B8
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. P(A and B) = 0.18, P(B) = 0.6. What is P(A given B)?

    Answer

  2. What does conditioning on B do?

    • It shrinks the sample space to just B.
    • It enlarges the sample space.

  3. P(A and B) = 0.3, P(B) = 0.6. P(A given B)?

    Answer

  4. P(A and B) = 0.12, P(B) = 0.4. P(A given B)?

    Answer

  5. 18 of 24 in a group have a trait. P(trait given the group)?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. P(A given B) = P(A). Independent? 1 yes, 0 no.

    Answer

  2. A die shows an even number. P(it is a 6), to three decimal places?

    Answer

  3. Is P(A given B) always equal to P(B given A)? 1 yes, 0 no.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Put the conditional probability method in order.

    Write 1 to 4 in the boxes to put these in order.

    • Identify which event is the condition.
    • Use that event as the new total.
    • Count how many of those also satisfy the other event.
    • Divide to get the conditional probability.

  2. P(A and B) = 0.35, P(B) = 0.7. P(A given B)?

    Answer

  3. The Condition

    P(A and B) = 0.2 and P(B) = 0.5. What is P(A given B)?

    Answer

  4. The Table

    Of 60 sport players, 45 play music. What is P(music given sport)?

    Answer